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%I #15 Feb 25 2024 11:11:24
%S 7,71,379,2659
%N Numbers k > 1 such that 2^(k-1) == (2*k + 1) (mod k^2).
%C No further terms up to 5 million. - _Harvey P. Dale_, Mar 20 2016
%C The definition implies 2^(k-1) == 1 (mod k), so all terms are either primes or Sarrus numbers (A001567). There are no further prime terms below 10^12, and no further Sarrus terms below 2^64. - _Lucas A. Brown_, Feb 19 2024
%H Jan Feitsma, <a href="https://web.archive.org/web/20130316150225/http://www.janfeitsma.nl/math/psp2/index">The pseudoprimes below 2^64</a>.
%t Select[Range[3000],PowerMod[2,#-1,#]==1&&PowerMod[2,#-1,#^2]-1==2*#&] (* _Harvey P. Dale_, Mar 20 2016 *)
%Y Cf. A001567, A128465.
%K nonn,hard,more
%O 1,1
%A _Alzhekeyev Ascar M_, Sep 30 2010